On one affine-invariant metric on the class of convex plane compacts

Theorem. For every plane convex compacts $K_1,K_2\subset\mathbb R^2$ there exist an affine transformations $T_1$, $T_2$ such that $T_1(K_1)\subset K_2\subset T_2(K_1)$ and $S(T_2(K_1))<111/16 S(T_1(K_1))$, where $S(K)$ means the square of a plane set $K\subset\mathbb R^2$.